From abc28fedba6d2b1a74a388424fd8beb400e47287 Mon Sep 17 00:00:00 2001 From: Joe Groff Date: Tue, 2 Feb 2010 00:30:21 -0800 Subject: [PATCH] vector-friendlier math.quaternions --- .../math/quaternions/quaternions-docs.factor | 27 ++----- .../math/quaternions/quaternions-tests.factor | 19 ++--- basis/math/quaternions/quaternions.factor | 76 ++++++++----------- 3 files changed, 51 insertions(+), 71 deletions(-) diff --git a/basis/math/quaternions/quaternions-docs.factor b/basis/math/quaternions/quaternions-docs.factor index a24011cb7c..1a381c6287 100644 --- a/basis/math/quaternions/quaternions-docs.factor +++ b/basis/math/quaternions/quaternions-docs.factor @@ -4,17 +4,17 @@ IN: math.quaternions HELP: q+ { $values { "u" "a quaternion" } { "v" "a quaternion" } { "u+v" "a quaternion" } } { $description "Add quaternions." } -{ $examples { $example "USING: math.quaternions prettyprint ;" "{ C{ 0 1 } 0 } { 0 1 } q+ ." "{ C{ 0 1 } 1 }" } } ; +{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 0 1 0 0 } { 0 0 1 0 } q+ ." "{ 0 1 1 0 }" } } ; HELP: q- { $values { "u" "a quaternion" } { "v" "a quaternion" } { "u-v" "a quaternion" } } { $description "Subtract quaternions." } -{ $examples { $example "USING: math.quaternions prettyprint ;" "{ C{ 0 1 } 0 } { 0 1 } q- ." "{ C{ 0 1 } -1 }" } } ; +{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 0 1 0 0 } { 0 0 1 0 } q- ." "{ 0 1 -1 0 }" } } ; HELP: q* { $values { "u" "a quaternion" } { "v" "a quaternion" } { "u*v" "a quaternion" } } { $description "Multiply quaternions." } -{ $examples { $example "USING: math.quaternions prettyprint ;" "{ C{ 0 1 } 0 } { 0 1 } q* ." "{ 0 C{ 0 1 } }" } } ; +{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 0 1 0 0 } { 0 0 1 0 } q* ." "{ 0 0 0 1 }" } } ; HELP: qconjugate { $values { "u" "a quaternion" } { "u'" "a quaternion" } } @@ -27,28 +27,17 @@ HELP: qrecip HELP: q/ { $values { "u" "a quaternion" } { "v" "a quaternion" } { "u/v" "a quaternion" } } { $description "Divide quaternions." } -{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 0 C{ 0 1 } } { 0 1 } q/ ." "{ C{ 0 1 } 0 }" } } ; +{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 0 0 0 1 } { 0 0 1 0 } q/ ." "{ 0 1 0 0 }" } } ; HELP: q*n -{ $values { "q" "a quaternion" } { "n" number } { "q" "a quaternion" } } -{ $description "Multiplies each element of " { $snippet "q" } " by " { $snippet "n" } "." } -{ $notes "You will get the wrong result if you try to multiply a quaternion by a complex number on the right using " { $link v*n } ". Use this word instead." - $nl "Note that " { $link v*n } " with a quaternion and a real is okay." } ; +{ $values { "q" "a quaternion" } { "n" real } { "q" "a quaternion" } } +{ $description "Multiplies each element of " { $snippet "q" } " by real value " { $snippet "n" } "." } +{ $notes "To multiply a quaternion with a complex value, use " { $link c>q } " " { $link q* } "." } ; HELP: c>q { $values { "c" number } { "q" "a quaternion" } } { $description "Turn a complex number into a quaternion." } -{ $examples { $example "USING: math.quaternions prettyprint ;" "C{ 0 1 } c>q ." "{ C{ 0 1 } 0 }" } } ; - -HELP: v>q -{ $values { "v" vector } { "q" "a quaternion" } } -{ $description "Turn a 3-vector into a quaternion with real part 0." } -{ $examples { $example "USING: math.quaternions prettyprint ;" "{ 1 0 0 } v>q ." "{ C{ 0 1 } 0 }" } } ; - -HELP: q>v -{ $values { "q" "a quaternion" } { "v" vector } } -{ $description "Get the vector part of a quaternion, discarding the real part." } -{ $examples { $example "USING: math.quaternions prettyprint ;" "{ C{ 0 1 } 0 } q>v ." "{ 1 0 0 }" } } ; +{ $examples { $example "USING: math.quaternions prettyprint ;" "C{ 0 1 } c>q ." "{ 0 1 0 0 }" } } ; HELP: euler { $values { "phi" number } { "theta" number } { "psi" number } { "q" "a quaternion" } } diff --git a/basis/math/quaternions/quaternions-tests.factor b/basis/math/quaternions/quaternions-tests.factor index 3efc417e42..b049b6dbc4 100644 --- a/basis/math/quaternions/quaternions-tests.factor +++ b/basis/math/quaternions/quaternions-tests.factor @@ -2,6 +2,12 @@ IN: math.quaternions.tests USING: tools.test math.quaternions kernel math.vectors math.constants ; +CONSTANT: q0 { 0 0 0 0 } +CONSTANT: q1 { 1 0 0 0 } +CONSTANT: qi { 0 1 0 0 } +CONSTANT: qj { 0 0 1 0 } +CONSTANT: qk { 0 0 0 1 } + [ 1.0 ] [ qi norm ] unit-test [ 1.0 ] [ qj norm ] unit-test [ 1.0 ] [ qk norm ] unit-test @@ -10,18 +16,13 @@ math.constants ; [ t ] [ qi qj q* qk = ] unit-test [ t ] [ qj qk q* qi = ] unit-test [ t ] [ qk qi q* qj = ] unit-test -[ t ] [ qi qi q* q1 v+ q0 = ] unit-test -[ t ] [ qj qj q* q1 v+ q0 = ] unit-test -[ t ] [ qk qk q* q1 v+ q0 = ] unit-test -[ t ] [ qi qj qk q* q* q1 v+ q0 = ] unit-test -[ t ] [ C{ 0 1 } qj n*v qk = ] unit-test -[ t ] [ qj C{ 0 1 } q*n qk v+ q0 = ] unit-test +[ t ] [ qi qi q* q1 q+ q0 = ] unit-test +[ t ] [ qj qj q* q1 q+ q0 = ] unit-test +[ t ] [ qk qk q* q1 q+ q0 = ] unit-test +[ t ] [ qi qj qk q* q* q1 q+ q0 = ] unit-test [ t ] [ qk qj q/ qi = ] unit-test [ t ] [ qi qk q/ qj = ] unit-test [ t ] [ qj qi q/ qk = ] unit-test -[ t ] [ qi q>v v>q qi = ] unit-test -[ t ] [ qj q>v v>q qj = ] unit-test -[ t ] [ qk q>v v>q qk = ] unit-test [ t ] [ 1 c>q q1 = ] unit-test [ t ] [ C{ 0 1 } c>q qi = ] unit-test [ t ] [ qi qi q+ qi 2 q*n = ] unit-test diff --git a/basis/math/quaternions/quaternions.factor b/basis/math/quaternions/quaternions.factor index b713f44ebd..0c94f4d119 100644 --- a/basis/math/quaternions/quaternions.factor +++ b/basis/math/quaternions/quaternions.factor @@ -1,72 +1,62 @@ ! Copyright (C) 2005, 2007 Slava Pestov. ! See http://factorcode.org/license.txt for BSD license. -USING: arrays kernel math math.functions math.vectors sequences ; +USING: arrays combinators kernel math math.functions math.libm math.vectors sequences ; IN: math.quaternions -! Everybody's favorite non-commutative skew field, the quaternions! - -! Quaternions are represented as pairs of complex numbers, using the -! identity: (a+bi)+(c+di)j = a+bi+cj+dk. - - - : q+ ( u v -- u+v ) - v+ ; + v+ ; inline : q- ( u v -- u-v ) - v- ; + v- ; inline : q* ( u v -- u*v ) - [ q*a ] [ q*b ] 2bi 2array ; + { + [ [ { 1 0 0 0 } vshuffle ] [ { 1 1 2 3 } vshuffle ] bi* v* ] + [ [ { 2 1 2 3 } vshuffle ] [ { 2 0 0 0 } vshuffle ] bi* v* v+ ] + [ [ { 3 2 3 1 } vshuffle ] [ { 3 3 1 2 } vshuffle ] bi* v* v+ ] + [ [ { 0 3 1 2 } vshuffle ] [ { 0 2 3 1 } vshuffle ] bi* v* v- ] + } 2cleave { -1 1 1 1 } v* ; inline : qconjugate ( u -- u' ) - first2 [ conjugate ] [ neg ] bi* 2array ; + { 1 -1 -1 -1 } v* ; inline : qrecip ( u -- 1/u ) - qconjugate dup norm-sq v/n ; + qconjugate dup norm-sq v/n ; inline : q/ ( u v -- u/v ) - qrecip q* ; + qrecip q* ; inline + +: n*q ( q n -- q ) + v*n ; inline : q*n ( q n -- q ) - conjugate v*n ; + v*n ; inline + +: n>q ( n -- q ) + 0 0 0 4array ; inline + +: n>q-like ( c exemplar -- q ) + [ 0 0 0 ] dip 4sequence ; inline : c>q ( c -- q ) - 0 2array ; + >rect 0 0 4array ; inline -: v>q ( v -- q ) - first3 rect> [ 0 swap rect> ] dip 2array ; - -: q>v ( q -- v ) - first2 [ imaginary-part ] dip >rect 3array ; - -! Zero -CONSTANT: q0 { 0 0 } - -! Units -CONSTANT: q1 { 1 0 } -CONSTANT: qi { C{ 0 1 } 0 } -CONSTANT: qj { 0 1 } -CONSTANT: qk { 0 C{ 0 1 } } +: c>q-like ( c exemplar -- q ) + [ >rect 0 0 ] dip 4sequence ; inline ! Euler angles q ] [ sin ] bi ] dip n*v v- ; +: (euler) ( theta exemplar shuffle -- q ) + swap + [ 0.5 * [ fcos ] [ fsin ] bi 0.0 0.0 ] [ call ] [ 4sequence ] tri* ; inline PRIVATE> +: euler-like ( phi theta psi exemplar -- q ) + [ [ ] (euler) ] [ [ swapd ] (euler) ] [ [ rot ] (euler) ] tri-curry tri* q* q* ; inline + : euler ( phi theta psi -- q ) - [ qi (euler) ] [ qj (euler) ] [ qk (euler) ] tri* q* q* ; + { } euler-like ; inline +